publications

New Paper: Stabilized mixed continuous/enriched Galerkin formulations for locally mass conservative poromechanics

Our paper on stabilized mixed CG/EG formulation for poromechanics has been accepted for publication in Computer Methods in Applied Mechanics and Engineering.

Read the paper: Choo, CMAME 2019. 

Abstract: Local (element-wise) mass conservation is often highly desired for numerical solution of coupled poromechanical problems. As an efficient numerical method featuring this property, mixed continuous Galerkin (CG)/enriched Galerkin (EG) finite elements have recently been proposed whereby piecewise constant functions are enriched to the pore pressure interpolation functions of the conventional mixed CG/CG elements. While this enrichment of the pressure space provides local mass conservation, it unavoidably alters the stability condition for mixed finite elements. Because no stabilization method has been available for the new stability condition, high-order displacement interpolation has been required for mixed CG/EG elements if undrained condition is expected. To circumvent this requirement, here we develop stabilized formulations for the mixed CG/EG elements that permit equal-order interpolation functions even in the undrained limit. We begin by identifying the inf–sup condition for mixed CG/EG elements by phrasing an enriched poromechanical problem as a twofold saddle point problem. We then derive two types of stabilized formulations, one based on the polynomial pressure projection (PPP) method and the other based on the fluid pressure Laplacian (FPL) method. A key finding of this work is that both methods lead to stabilization terms that should be augmented only to the CG part of the pore pressure field, not to the enrichment part. The two stabilized formulations are verified and investigated through numerical examples involving various conditions ranging from 1D to 3D, isotropy to anisotropy, and homogeneous to heterogeneous domains. The methodology presented in this work may also help stabilize other types of mixed finite elements in which the constraint field is enriched by additional functions.

New paper: Mohr–Coulomb plasticity for sands incorporating density effects without parameter calibration

Our paper on simple Mohr–Coulomb plasticity for capturing density effects on sand has been accepted for publication in International Journal for Numerical and Analytical Methods in Geomechanics.

Read the paper: Choo, IJNAMG 2018.

Abstract: A simple approach is proposed for enabling the conventional Mohr–Coulomb plasticity to capture the effects of relative density on the behavior of dilative sands. The approach exploits Bolton's empirical equations to make friction and dilation angles state variables that depend on the current density and confining pressure. In doing so, the material parameters of Mohr–Coulomb plasticity become void ratios for calculating the initial relative density and the critical state friction angle, all of which are measurable without calibration. A Mohr–Coulomb model enhanced in this way shows good agreement with experimental data of different sands at various densities and confining pressures. In this regard, the proposed approach permits a significant improvement in the conventional Mohr–Coulomb plasticity for sands, without compromising its practical merits.

New paper: Liquid CO2 fracturing: Effect of fluid permeation on the breakdown pressure and cracking behavior

Our paper on liquid CO2 fracturing, in collaboration with Prof. Tae Sup Yun at Yonsei University, has been accepted for publication in Rock Mechanics and Rock Engineering.

Read the paper: Ha et al., RMRE 2018. 

Abstract: Liquid CO2 fracturing is a promising alternative to hydraulic fracturing since it can circumvent problems stemming from the use of water. One of the most significant differences between liquid CO2 and hydraulic fracturing processes is that liquid CO2 permeates into matrix pores very rapidly due to its low viscosity. Here we study how this rapid permeation of liquid CO2 impacts a range of features during the course of the fracturing process, with a focus on the breakdown pressure and cracking behavior. We first conduct a series of laboratory fracturing experiments that inject liquid CO2, water, and oil into nominally identical mortar specimens with various pressurization rates. We quantitatively measure the volumes of fluids permeated into the specimens and investigate how these permeated volumes are related to breakdown and fracture initiation pressures and pressurization efficiency. The morphology of the fractures generated by different types of fluids are also examined using 3D X-ray computed tomographic imaging. Subsequently, the cracking processes due to injection of liquid CO2 and water are further investigated by numerical simulations employing a phase-field approach to fracture in porous media. Simulation results show that rapid permeation of liquid CO2 gives rise to a substantial pore pressure buildup and distributed microcracks prior to the major fracture propagation stage. The experimental and numerical results commonly indicate that significant fluid permeation during liquid CO2 fracturing is a primary reason for its lower breakdown pressure and more distributed fractures compared with hydraulic fracturing.

Simulation of liquid CO2 fracturing in a heterogeneous brittle porous material. The red zone denotes fully cracked regions, whereas the blue zone denotes intact regions. The green zone denotes microcracked regions. The video shows that the injection of liquid CO2 — which involves a huge amount of fluid permeation into the matrix — gives rise to a lot of microcracks prior to fracture propagation.

Simulation of hydraulic (water) fracturing in the same porous material. The video shows that when the same material is fractured by the injection of water, virtually no microcrack develops in the matrix before and during the fracture propagation stage. As a result, this process manifests a higher breakdown pressure, as observed from experiments of our collaborator and others.

New paper: Large deformation poromechanics with local mass conservation: An enriched Galerkin finite element framework

Our paper on locally mass conservative finite element framework for large deformation poromechanics has been accepted for publication in International Journal for Numerical Methods in Engineering.

Read the paper: Choo, IJNME 2018.

Abstract: Numerical modeling of large deformations in fluid-infiltrated porous media must accurately describe not only geometrically nonlinear kinematics but also fluid flow in heterogeneously deforming pore structure. Accurate simulation of fluid flow in heterogeneous porous media often requires a numerical method that features the local (element-wise) conservation property. Here we introduce a new finite element framework for locally mass conservative solution of coupled poromechanical problems at large strains. At the core of our approach is the enriched Galerkin discretization of the fluid mass balance equation, whereby element-wise constant functions are augmented to the standard continuous Galerkin discretization. The resulting numerical method provides local mass conservation by construction, with a usually affordable cost added to the continuous Galerkin counterpart. Two equivalent formulations are developed using total Lagrangian and updated Lagrangian approaches. The local mass conservation property of the proposed method is verified through numerical examples involving saturated and unsaturated flow in porous media at finite strains. The numerical examples also demonstrate that local mass conservation can be a critical element of accurate simulation of both fluid flow and large deformation in porous media.

This paper proposes the first locally mass conservative finite element framework for large deformation poromechanical problems. The formulation builds on our previous work on enriched Galerkin (EG) methods. This figure shows local (element-wise) mass residuals in a synthetic land subsidence problem due to groundwater withdrawal. It can be seen that the local mass residuals are significant in the conventional continuous Galerkin (CG) solutions, but they become nearly zero in the EG solutions. This difference also affects the predicted subsidence results. The property of local mass conservation can become far more important once the flow is coupled with a transport phenomenon.

This paper proposes the first locally mass conservative finite element framework for large deformation poromechanical problems. The formulation builds on our previous work on enriched Galerkin (EG) methods. This figure shows local (element-wise) mass residuals in a synthetic land subsidence problem due to groundwater withdrawal. It can be seen that the local mass residuals are significant in the conventional continuous Galerkin (CG) solutions, but they become nearly zero in the EG solutions. This difference also affects the predicted subsidence results. The property of local mass conservation can become far more important once the flow is coupled with a transport phenomenon.

New paper: Enriched Galerkin finite elements for coupled poromechanics with local mass conservation

Our paper on enriched Galerkin finite element methods for coupled poromechanics, in collaboration with Prof. Sanghyun Lee at Florida State University, has been accepted for publication in Computer Methods in Applied Mechanics and Engineering.

Read the paper: Choo and Lee, CMAME 2018.

Abstract: Robust and efficient discretization methods for coupled poromechanical problems are critical to address a wide range of problems related to civil infrastructure, energy resources, and environmental sustainability. In this work, we propose a new finite element formulation for coupled poromechanical problems that ensures local (element-wise) mass conservation. The proposed formulation draws on the so-called enriched Galerkin method, which augments piecewise constant functions to the classical continuous Galerkin finite element method. These additional degrees of freedom allow us to obtain a locally conservative and nonconforming solution for the pore pressure field. The enriched and continuous Galerkin formulations are compared in several numerical examples ranging from a benchmark consolidation problem to a complex problem that involves plastic deformation due to unsaturated flow in a heterogeneous porous medium. The results of these examples show not only that the proposed method provides local mass conservation, but also that local mass conservation can be crucial to accurate simulation of deformation processes in fluid-infiltrated porous materials.

This work introduces enriched Galerkin (EG) finite element methods for locally mass conservative solution of coupled poromechanics problems. Shown above is EG solution of an unsaturated flow problem in a heterogeneous soil domain. Fluid mass is conserved locally (element-wise) in this pressure field. However, when the same problem is solved by the standard continuous Galerkin (CG) method, the simulation result is significantly different, and fluid mass shows nontrivial imbalances in many elements. This difference also impacts the deformation response of the problem.

This work introduces enriched Galerkin (EG) finite element methods for locally mass conservative solution of coupled poromechanics problems. Shown above is EG solution of an unsaturated flow problem in a heterogeneous soil domain. Fluid mass is conserved locally (element-wise) in this pressure field. However, when the same problem is solved by the standard continuous Galerkin (CG) method, the simulation result is significantly different, and fluid mass shows nontrivial imbalances in many elements. This difference also impacts the deformation response of the problem.